[QE-users] High-symmetry points in Band Structure plot

[MARIA CATERINA CEVALLOS BRENES]

El 27-12-2018 14:37, Josue Itsman Clavijo Penagos escribió:

> Dear Maria, have a nice research day. Before trying an answer to your questions, a kind  reminder of some posting guidelines: 
> 
> Please always include you affiliation/granting institute. 
> 
> Present yourself politely, and insofar do not link to other forum/posts outside QE-users mailing lists; it's not neither nice nor common practice to do that. 
> 
> Now, regarding your questioning, high-simmetry points in reciprocal space are used becaused they best describe the simplest (and the shortest, as far as I remember) paths a travelling periodic wave (bloch solutions) can take to move out through the crystal; the precise location of those points depends on the space group the crystal structure shows. 
> 
> So if one study the Band structure at those high-simmetry points, bassically all the E-k relationship are determined for electrons in the material under study. 
> 
> On the computing side,  bands.x produces a x-coordinate values sequence to map the k points path in the same order you have specified previously; so, if your set the following path for the Si primitive cell (as recommended in HINUMA _ET AL_, _Band structure diagram paths based on crystallography_, HTTPS://ARXIV.ORG/ABS/1602.06402, there are two different recommended k-paths for Si, not connected by shortest distances between the U and K points) 
> 
> K_POINTS crystal_b 
> 
> 0.0000000000 0.0000000000 0.0000000000 10 
> 0.5000000000 0.0000000000 0.5000000000 10 
> 0.6250000000 0.2500000000 0.6250000000 1 
> 0.3750000000 0.3750000000 0.7500000000 10 
> 0.0000000000 0.0000000000 0.0000000000 10 
> 0.5000000000 0.5000000000 0.5000000000 10 
> 0.5000000000 0.2500000000 0.7500000000 10 
> 0.5000000000 0.0000000000 0.5000000000 1 
> 
> bands.x will generate  
> 
> 10 intermediate k-points in between Gamma->X (Beginning of first path) 
> 10 intermediate k-points in between X->U 
> 1 k-point at U (End of first path) (When you plot, draw a thick vertical line at this point to make clear this is the end of the path and that there is no connection with the next point - K - also). 
> 10 intermediate k-points in between K-->Gamma (Beginning of second path) 
> 10 intermediate k-points in between Gamma->L 
> 10 intermediate k-points in between L->W 
> 10 intermediate k-points in between W->X 
> 1 k-point at X (end of second path) 
> 
> That is, 62 k-points for the recommended paths Γ--X--U|K--Γ--L--W--X. 
> 
> By the way, the plot you show in physics.stackexchange.com [1] uses a custom selected k-path. One can choose the k-path that best fits/likes oneself, but the recommended one is just enough. Citing the hinuma _et al_ paper, the recommend k-path is the one that "_cover all special wavevector (k -vector) points and lines necessarily and sufficiently_". 
> 
> So you can see/copy/build the suggested k-points path for your different structures by uploading your *.cif/*.pw.in [2] files in https://www.materialscloud.org/work/tools/seekpath 
> 
> Hope all of this helps. 
> 
> Best regards and happy holydays! 
> 
> _PROFESSOR JOSUÉ CLAVIJO, PH.D._ 
> 
> CHRISTIAN, BORN AGAIN
> 
> _Assistant Professor_ 
> Universidad Nacional de Colombia 
> Bogotá DC 
> Facultad de Ciencias 
> Departamento de Química 
> 571-3165000 Ext. 14445 
> 
> josue.clavijo at gmail.com
> jiclavijop at unal.edu.co 
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Thanks Mr Clavijo. This solved the question I had. 

I'm sorry I didn't present myself properly, I honestly wasn't aware of
the guidelines. And the reason I put the link instead of writing my
question here was due to format. 

By using the institutional mail I cannot put images in certain order,
just attach them. And also the code chunks look better in that
particular web forum. But in any case I won't do it again. 

Have a nice day and thanks for your help. 

Kind regards, 

María. 

  

Links:
------
[1] http://physics.stackexchange.com
[2] http://pw.in
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